Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 396267, 14 pages
Research Article

Collision and Stable Regions around Bodies with Simple Geometric Shape

1Space Mechanics and Control Division (DMC), National Institute for Space Research (INPE), São José dos Campos 12227-010, Brazil
2UNESP, Universidade Estadual Paulista , Grupo de Dinâmica Orbital & Planetologia, Av. Ariberto Pereira da Cunha, 333-Guaratinguetá 12516-410, Brazil
3Universidade do Vale do Paraíba (CT I / UNIVAP), São José dos Campos 12245-020, Brazil

Received 29 July 2009; Accepted 20 October 2009

Academic Editor: Silvia Maria Giuliatti Winter

Copyright © 2009 A. A. Silva et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We show the expressions of the gravitational potential of homogeneous bodies with well-defined simple geometric shapes to study the phase space of trajectories around these bodies. The potentials of the rectangular and triangular plates are presented. With these expressions we study the phase space of trajectories of a point of mass around the plates, using the Poincaré surface of section technique. We determined the location and the size of the stable and collision regions in the phase space, and the identification of some resonances. This work is the first and an important step for others studies, considering 3D bodies. The study of the behavior of a point of mass orbiting around these plates (2D), near their corners, can be used as a parameter to understand the influence of the gravitational potential when the particle is close to an irregular surface, such as large craters and ridges.